### Araştırma Makalesi

IUP :10.26650/ijmath.2024.00015    Tam Metin (PDF)

# Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method

This work presents a unique technique for the precise and efficient solution of Linear Fredholm integro-differential equations (LFDEs), the technique is based on the Modification of Adomian Decomposition Method (MADM). The MADM extends the well-known Adomian Decomposition Method (ADM) by integrating novel changes that improve convergence and computing efficiency. The LFDEs are essential for simulating a wide range of phenomena in science and engineering. Because their analytical solutions are frequently difficult to achieve, the development of efficient and trustworthy numerical approaches is required. We present an introduction of the MADM method and its important characteristics emphasizing its capacity to handle a wide range of LFDEs seen in scientific and engineering applications. We demonstrate the method’s usefulness in contrast to the true approach, stressing its computational benefits and precision.

Anahtar Kelimeler: Computational Efficiency

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#### Atıflar

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##### APA

Kareem, K.O., Olayiwola, M.O., Ogunnıran, M.O., Oladapo, A.O., Yunus, A.O., Adedokun, K.A., Adedeji, J.A., & Alaje, I.A. (2024). Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method. Istanbul Journal of Mathematics, 2(1), 44-54. https://doi.org/10.26650/ijmath.2024.00015

##### AMA

Kareem K O, Olayiwola M O, Ogunnıran M O, Oladapo A O, Yunus A O, Adedokun K A, Adedeji J A, Alaje I A. Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method. Istanbul Journal of Mathematics. 2024;2(1):44-54. https://doi.org/10.26650/ijmath.2024.00015

##### ABNT

Kareem, K.O.; Olayiwola, M.O.; Ogunnıran, M.O.; Oladapo, A.O.; Yunus, A.O.; Adedokun, K.A.; Adedeji, J.A.; Alaje, I.A. Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method. Istanbul Journal of Mathematics, [Publisher Location], v. 2, n. 1, p. 44-54, 2024.

##### Chicago: Author-Date Style

Kareem, Kabiru Oyeleye, and Morufu Oyedunsi Olayiwola and Muideen Odunayo Ogunnıran and Asimiyu Olalekan Oladapo and Akeem Olanrewaju Yunus and Kamilu Adewale Adedokun and Joseph Adeleke Adedeji and Ismail Adedapo Alaje. 2024. “Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method.” Istanbul Journal of Mathematics 2, no. 1: 44-54. https://doi.org/10.26650/ijmath.2024.00015

##### Chicago: Humanities Style

Kareem, Kabiru Oyeleye, and Morufu Oyedunsi Olayiwola and Muideen Odunayo Ogunnıran and Asimiyu Olalekan Oladapo and Akeem Olanrewaju Yunus and Kamilu Adewale Adedokun and Joseph Adeleke Adedeji and Ismail Adedapo Alaje. Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method.” Istanbul Journal of Mathematics 2, no. 1 (Aug. 2024): 44-54. https://doi.org/10.26650/ijmath.2024.00015

##### Harvard: Australian Style

Kareem, KO & Olayiwola, MO & Ogunnıran, MO & Oladapo, AO & Yunus, AO & Adedokun, KA & Adedeji, JA & Alaje, IA 2024, 'Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method', Istanbul Journal of Mathematics, vol. 2, no. 1, pp. 44-54, viewed 11 Aug. 2024, https://doi.org/10.26650/ijmath.2024.00015

##### Harvard: Author-Date Style

Kareem, K.O. and Olayiwola, M.O. and Ogunnıran, M.O. and Oladapo, A.O. and Yunus, A.O. and Adedokun, K.A. and Adedeji, J.A. and Alaje, I.A. (2024) ‘Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method’, Istanbul Journal of Mathematics, 2(1), pp. 44-54. https://doi.org/10.26650/ijmath.2024.00015 (11 Aug. 2024).

##### MLA

Kareem, Kabiru Oyeleye, and Morufu Oyedunsi Olayiwola and Muideen Odunayo Ogunnıran and Asimiyu Olalekan Oladapo and Akeem Olanrewaju Yunus and Kamilu Adewale Adedokun and Joseph Adeleke Adedeji and Ismail Adedapo Alaje. Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method.” Istanbul Journal of Mathematics, vol. 2, no. 1, 2024, pp. 44-54. [Database Container], https://doi.org/10.26650/ijmath.2024.00015

##### Vancouver

Kareem KO, Olayiwola MO, Ogunnıran MO, Oladapo AO, Yunus AO, Adedokun KA, Adedeji JA, Alaje IA. Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method. Istanbul Journal of Mathematics [Internet]. 11 Aug. 2024 [cited 11 Aug. 2024];2(1):44-54. Available from: https://doi.org/10.26650/ijmath.2024.00015 doi: 10.26650/ijmath.2024.00015

Kareem, KabiruOyeleye - Olayiwola, MorufuOyedunsi - Ogunnıran, MuideenOdunayo - Oladapo, AsimiyuOlalekan - Yunus, AkeemOlanrewaju - Adedokun, KamiluAdewale - Adedeji, JosephAdeleke - Alaje, IsmailAdedapo. Approximating Higher Order Linear Fredholm Integro-Differential Equations by an Efficient Adomian Decomposition Method”. Istanbul Journal of Mathematics 2/1 (Aug. 2024): 44-54. https://doi.org/10.26650/ijmath.2024.00015

### ZAMAN ÇİZELGESİ

 Gönderim 04.02.2024 Kabul 10.06.2024 Çevrimiçi Yayınlanma 25.06.2024